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Capacity planning in a semiconductor wafer fabrication facility with time constraints between process steps

Jennifer K Robinson, University of Massachusetts Amherst


Central to the advancement of the U.S. economy is the efficient production of semiconductors, which in turn depends upon having accurate methods of planning semiconductor wafer fabrication facility capacity. A characteristic of water fabrication that makes capacity planning particularly difficult is the presence of time constraints between process steps, also known as time bound sequences. In a time bound sequence, there exists a step that must be completed within some fixed time interval of an earlier step. An example in semiconductor manufacturing is a furnace operation that must be started within two hours of a prior clean operation. If more than two hours elapse before the furnace operation can begin, the job must be sent back to the clean operation for reprocessing. The capacity of a time bound sequence can be difficult to predict. At low equipment utilizations, lots flow through with few delays, and are rarely sent back for reprocessing. At higher arrival rates, however, or for highly variable systems, time bound sequences can rapidly become unstable. To know the capacity of some time bound sequences requires knowing the entire distribution of lot cycle times. This research uses simulation to understand the behavior of time bound sequences, and then develops analytic models to estimate their capacity. This dissertation focuses first on the simplest type of the bound sequences, those that involve only two operations. For such sequences, the time constraint only applies to the time in queue for the second operation. In this case, a simple approximation based on M/M/c queueing formulas is shown to perform quite well in predicting the probability of reprocessing. This approximation provides a bound that can easily be included in spreadsheet capacity models. A fluid model is then developed for the more complex situation of time bound sequences with intermediate operations. Based on the behavior of the model, several practical guidelines are given for planning capacity in the presence of time bound sequences. The most significant of these guidelines is a method for selecting time constraint values for which the probability of reprocessing is very small, so that systems will be well-behaved.

Subject Area

Industrial engineering|Operations research

Recommended Citation

Robinson, Jennifer K, "Capacity planning in a semiconductor wafer fabrication facility with time constraints between process steps" (1998). Doctoral Dissertations Available from Proquest. AAI9909212.